To solve the expression [tex]\(3 \sqrt{2 \cdot 5}\)[/tex], we need to follow a sequence of mathematical steps. Let’s break it down:
1. Inner Multiplication:
- First, we need to work out the product inside the square root, which is [tex]\(2 \cdot 5\)[/tex].
- Calculating [tex]\(2 \cdot 5\)[/tex], we get [tex]\(10\)[/tex].
2. Square Root:
- Next, we take the square root of the result from step 1.
- The square root of [tex]\(10\)[/tex] is approximately [tex]\(3.1622776601683795\)[/tex].
3. Outer Multiplication:
- Finally, we multiply this square root by the coefficient outside, which is [tex]\(3\)[/tex].
- Calculating [tex]\(3 \cdot 3.1622776601683795\)[/tex], we get approximately [tex]\(9.486832980505138\)[/tex].
So, the computed result of the expression [tex]\(3 \sqrt{2 \cdot 5}\)[/tex] is approximately [tex]\(9.486832980505138\)[/tex].
